GEOMETRY OFSTRAIGHT LINES

Exercise MEMOSTopic 10

GEOMETRY OFSTRAIGHT LINES

Ex 10.1 MEMOTopic 10

EXERCISE 10.1 Pg. 87 Calculate the unknown angles in each of the following, giving reasons for all your statements

Statement Reason

𝒙 + 𝟓𝟓° = 𝟏𝟖𝟎° ∠′𝒔 𝒐𝒏 𝒂 𝒔𝒕𝒓 𝒍𝒊𝒏𝒆𝒙 = 𝟏𝟖𝟎° − 𝟓𝟓 °𝒙 = 𝟏𝟐𝟓°

𝒙 = 𝟗𝟓° 𝑽𝒆𝒓𝒕 𝒐𝒑𝒑 ∠′𝒔 =

𝟒𝟓° + 𝒙 + 𝟒𝟎° = 𝟏𝟖𝟎° ∠′𝒔 𝒐𝒏 𝒂 𝒔𝒕𝒓 𝒍𝒊𝒏𝒆𝒙 = 𝟏𝟖𝟎° − 𝟒𝟓° − 𝟒𝟎°𝒙 = 𝟗𝟓°

Statement Reason

𝟐𝒙 + 𝟗𝟎° = 𝟏𝟖𝟎° ∠′𝒔 𝒐𝒏 𝒂 𝒔𝒕𝒓 𝒍𝒊𝒏𝒆𝟐𝒙 = 𝟏𝟖𝟎° − 𝟗𝟎 °𝟐𝒙 = 𝟗𝟎°𝒙 = 𝟒𝟓°

𝒙 = 𝟑𝟎° + 𝟓𝟎° 𝑽𝒆𝒓𝒕 𝒐𝒑𝒑 ∠′𝒔 =𝒙 = 𝟖𝟎°

𝒙 + 𝟕𝟎° = 𝟏𝟖𝟎° ∠′𝒔 𝒐𝒏 𝒂 𝒔𝒕𝒓 𝒍𝒊𝒏𝒆𝒙 = 𝟏𝟖𝟎° − 𝟕𝟎°𝒙 = 𝟏𝟏𝟎°

𝒚 + 𝟏𝟎° = 𝟏𝟖𝟎° ∠′𝒔 𝒐𝒏 𝒂 𝒔𝒕𝒓 𝒍𝒊𝒏𝒆𝒚 = 𝟏𝟖𝟎° − 𝟏𝟎°𝒚 = 𝟏𝟕𝟎°

EXERCISE 10.1 Pg. 87 Calculate the unknown angles in each of the following, giving reasons for all your statements

Statement Reason𝒚 + 𝟏𝟒𝟎° = 𝟏𝟖𝟎° ∠′𝒔 𝒐𝒏 𝒂 𝒔𝒕𝒓 𝒍𝒊𝒏𝒆𝒚 = 𝟏𝟖𝟎° − 𝟏𝟒𝟎 °𝒚 = 𝟒𝟎°

𝒙 + 𝒚 + 𝟏𝟏𝟎° = 𝟏𝟖𝟎° ∠′𝒔 𝒐𝒏 𝒂 𝒔𝒕𝒓 𝒍𝒊𝒏𝒆𝒙 + 𝟒𝟎° + 𝟏𝟏𝟎° = 𝟏𝟖𝟎 °𝒙 = 𝟏𝟖𝟎° − 𝟒𝟎° − 𝟏𝟏𝟎°𝒙 = 𝟑𝟎°

𝒙 = 𝟐𝟓° 𝑽𝒆𝒓𝒕 𝒐𝒑𝒑 ∠′𝒔 =

𝒚 = 𝟏𝟒𝟎° 𝑽𝒆𝒓𝒕 𝒐𝒑𝒑 ∠′𝒔 =

𝒙 + 𝟏𝟒𝟎° + 𝒛 = 𝟏𝟖𝟎°𝟐𝟓° + 𝟏𝟒𝟎° + 𝒛 = 𝟏𝟖𝟎°𝒛 = 𝟏𝟖𝟎° − 𝟏𝟒𝟎° − 𝟐𝟓°𝒛 = 𝟏𝟓°

EXERCISE 10.1 Pg. 87 Calculate the unknown angles in each of the following, giving reasons for all your statements

GEOMETRY OFSTRAIGHT LINES

Ex 10.2 MEMOTopic 10

EXERCISE 10.2 Pg. 91

1. State whether lines AB and CD are parallel in the following diagrams, with reasons.

𝑨𝑩 ∦ 𝑪𝑫(AB not parallel to CD)

𝑨𝒍𝒕 ∠′𝒔 ≠(Alternating Angles not Equal)

𝑨𝑩 ∥ 𝑪𝑫𝑨𝒍𝒕 ∠′𝒔 =

𝑨𝑩 ∥ 𝑪𝑫𝑪𝒐𝒓𝒓 ∠′𝒔 =

𝑨𝑩 ∥ 𝑪𝑫𝑪𝒐 − 𝒊𝒏𝒕 ∠′𝒔 𝒔𝒖𝒑𝒑

EXERCISE 10.2 Pg. 91

2. Calculate the unknown angles in each of the following, giving reasons for all your statements

Statement Reason

𝒙 = 𝟖𝟎° 𝑪𝒐𝒓𝒓 ∠′𝒔 =; 𝑬𝑭 ∥ 𝑪𝑫

Statement Reason

𝒙 = 𝟑𝟓° 𝐀𝐥𝐭 ∠′𝒔 =;𝑫𝑬 ∥ 𝑭𝑮

Statement Reason

𝒙 + 𝟒𝟎 = 𝟏𝟖𝟎° 𝐂𝐨 − 𝐢𝐧𝐭 ∠′𝒔 𝒔𝒖𝒑𝒑;𝑨𝑩 ∥ 𝑪𝑫𝒙 = 𝟏𝟖𝟎° − 𝟒𝟎°𝒙 = 𝟏𝟒𝟎°

GEOMETRY OFSTRAIGHT LINES

Ex 10.3 MEMOTopic 10

EXERCISE 10.3 Pg. 95 (No. 1,2,3)

a.) መ𝐴1 = 20 𝐴𝑙𝑡∠′𝑠 = 𝐴𝐶 ∥ 𝐸𝐷

b.) መ𝐴2 = 70 𝐴𝑑𝑗 𝐶𝑜𝑚𝑝 ∠′𝑠(Angles Add up to 90)

c.) 𝐵1 = 70 𝐴𝑙𝑡∠′𝑠 = 𝐴𝐶 ∥ 𝐹𝐵

d.) 𝐵2 + 85 = 180 ∠′𝑠 𝑜𝑛 𝑎 𝑠𝑡𝑟 𝑙𝑖𝑛𝑒𝐵2 = 180 − 85𝐵2 = 95

e.) መ𝐶1 = 85 𝐴𝑙𝑡∠′𝑠 = 𝐴𝐶 ∥ 𝐹𝐵

f.) 𝐷1 = 95 𝐶𝑜 − 𝑖𝑛𝑡∠′𝑠 𝑠𝑢𝑝𝑝; 𝐹𝐵 ∥ 𝐸𝐷

2.) Determine the unknown values in the following diagrams, giving reasons for your statements.

a)

b)

EXERCISE 10.3 Pg. 95

45° + 25° + 2𝑥 − 10° = 180° 𝐶𝑜 − 𝑖𝑛𝑡∠′𝑠 𝑠𝑢𝑝𝑝; 𝐺𝐻 ∥ 𝐷𝐸2𝑥 = 180° − 45° − 25° + 10°2𝑥 = 120°𝑥 = 60°

𝑦 − 35° + 25° = 180° ∠′𝑠 𝑜𝑛 𝑎 𝑠𝑡𝑟 𝑙𝑖𝑛𝑒𝑦 = 180 + 35 − 25𝑦 = 190

3𝑥 + 𝑥 = 180° 𝐶𝑜 − 𝑖𝑛𝑡∠′𝑠 𝑠𝑢𝑝𝑝; 𝐴𝐵 ∥ 𝐶𝐷4𝑥 = 180°𝑥 = 45°

2.) Determine the unknown values in the following diagrams, giving reasons for your statements.

c)

d)

EXERCISE 10.3 Pg. 95

𝟐𝒙

𝟐𝒙

𝐵 መ𝐴𝐶 = 2𝑥 ∠′𝑠 𝑜𝑝𝑝 = 𝑠𝑖𝑑𝑒𝑠

𝐴 መ𝐶𝐷 = 2𝑥 𝐴𝑙𝑡 ∠′𝑠 =; 𝐴𝐵 ∥ 𝐷𝐶

30° + 80° + 2𝑥 = 180° ∠′𝑠 𝑖𝑛 𝑎 ∆2𝑥 = 180° − 30° − 80°2𝑥 = 70°𝑥 = 35°

𝐷 𝐸𝐹 = 𝑥 𝐴𝑙𝑡 ∠′𝑠 =; 𝐴𝐵 ∥ 𝐷𝐶

𝑥 + 20° + 𝑥 + 2𝑥 = 180° ∠′𝑠 𝑜𝑛 𝑎 𝑠𝑡𝑟 𝑙𝑖𝑛𝑒4𝑥 + 20° = 180°4𝑥 = 180° − 20°4𝑥 = 160°𝑥 = 40°

𝒙

3.) Consider the parallelogram ABCD, and determine the values of 𝑥, 𝑦 and 𝑧.

EXERCISE 10.3 Pg. 95

A B

DC E

2𝑥 + 10°

110° 𝑧5𝑦

Statement Reason2𝑥 + 10° = 110° 𝑂𝑝𝑝 ∠′𝑠 𝑜𝑓 𝑎 𝑝𝑎𝑟𝑚 𝑎𝑟𝑒 =2𝑥 = 110° − 10°2𝑥 = 100°𝑥 = 50°

Statement Reason2𝑥 + 10° + 5𝑦 = 180° 𝐶𝑜 − 𝑖𝑛𝑡 ∠′𝑠 𝑆𝑢𝑝𝑝; 𝐴𝐵 ∥ 𝐶𝐷2 50° + 10° + 5𝑦 = 180°100° + 10° + 5𝑦 = 180°5𝑦 = 180° − 100° − 10°5𝑦 = 70°𝑦 = 14°

Statement Reason5𝑦 + 𝑧 = 180° ∠′𝑠 𝑜𝑛 𝑎 𝑠𝑡𝑟 𝑙𝑖𝑛𝑒5 14° + 𝑧 = 180°70° + 𝑧 = 180°𝑧 = 180° − 70°𝑧 = 110°

GEOMETRY OFSTRAIGHT LINES

Rev Ex MEMOTopic 10

REVISION EXERCISE Pg. 97 (No.1e-h, 2a-b)

Statement Reason2𝑥 + 30° + 𝑥 = 180° ∠′𝑠 𝑜𝑛 𝑎 𝑠𝑡𝑟 𝑙𝑖𝑛𝑒3𝑥 = 180° − 30°3𝑥 = 150°𝑥 = 50°

𝑦 = 2𝑥 𝑉𝑒𝑟𝑡 𝑂𝑝𝑝 ∠′𝑠 =𝑦 = 2(50°)𝑦 = 100°

𝑥 + 15° = 45° 𝐴𝑙𝑡∠′𝑠 =; 𝐴𝐵 ∥ 𝐶𝐷𝑥 = 45° − 15°𝑥 = 30°

REVISION EXERCISE Pg. 97 (No.1e-h, 2a-b)

Statement Reason𝑥 = 50° 𝐴𝑙𝑡∠′𝑠 =; 𝑅𝑄 ∥ 𝑇𝑉

𝑆 𝑇𝑈 = 𝑥 = 50° ∠′𝑠 𝑜𝑝𝑝 = 𝑠𝑖𝑑𝑒𝑠

4𝑦 + 𝑥 + 𝑥 = 180° ∠′𝑠 𝑖𝑛 𝑎 ∆4𝑦 + 50° + 50° = 1804𝑦 + 100° = 180°4𝑦 = 180° − 100°4𝑦 = 80°𝑦 = 20°

𝑧 + 4𝑦 = 180° ∠′𝑠 𝑜𝑛 𝑎 𝑠𝑡𝑟 𝑙𝑖𝑛𝑒𝑧 + 4 20° = 180°𝑧 + 80° = 180°𝑧 = 180° − 80°𝑧 = 100°

𝒙

REVISION EXERCISE Pg. 97 (No.1e-h, 2a-b)

Statement Reason𝐿 𝑃𝑁 + 160° = 180° ∠′𝑠 𝑜𝑛 𝑎 𝑠𝑡𝑟 𝑙𝑖𝑛𝑒𝐿 𝑃𝑁 = 180° − 160°𝐿 𝑃𝑁 = 20°

2𝑥 = 20° 𝐴𝑙𝑡∠′𝑠 =;𝐾𝐿 ∥ 𝑀𝑁𝑥 = 10°

𝟐𝟎°

REVISION EXERCISE Pg. 97 (No.1e-h, 2a-b)

Statement Reason𝑥 + 𝐷 𝐸𝐶 + 90° = 180° ∠′𝑠 𝑜𝑛 𝑎 𝑠𝑡𝑟 𝑙𝑖𝑛𝑒𝐷 𝐸𝐶 = 180° − 90° − 𝑥𝐷 𝐸𝐶 = 90° − 𝑥

𝐺 𝐿𝐾 + 𝑥 = 180° 𝐶𝑜 − 𝑖𝑛𝑡 ∠′𝑠 =;𝐷𝐸 ∥ 𝐹𝐺𝐺𝐿𝐾 = 180° − 𝑥